Duality Symmetry in Kaluza-Klein $n+D+d$ Dimensional Cosmological Model

TL;DR

This paper demonstrates a duality symmetry in higher-dimensional cosmological models, showing invariance of the Einstein-Hilbert action under scale factor transformations, with detailed analysis of a specific 2+D+d dimensional case.

Contribution

It reveals a duality symmetry in the Einstein-Hilbert action for n+D+d dimensional models, extending understanding of invariances in higher-dimensional cosmology.

Findings

Invariance under duality transformation for n ≠ 2

Detailed analysis of 2+D+d dimensional model

Identification of symmetry in scale factors and scalar fields

Abstract

It is shown that, with the only exception of $n=2$, the Einstein-Hilbert action in $n+D+d$ dimensions, with $n$ times, is invariant under the duality transformation $a\to \frac{1}{a}$ and $b\to \frac{1}{b}$, where $a$ is a Friedmann-Robertson-Walker scale factor in $D$ dimensions and $b$ a Brans-Dicke scalar field in $d$ dimensions respectively. We investigate the $2+D+d$ dimensional cosmological model in some detail.